In this article, we find the different sufficient conditions for a compact minimal hypersurface $ M $ of the unit sphere $ S^{n+1}, n\in \mathbb{Z}^{+} $ to be the Clifford hypersurface $ S^{\ell }(\sqrt{\frac{\ell }{n}})\times S^{m}(\sqrt{\frac{m}{n}}), $ where $ \ell, m\in \mathbb{Z}^{+}, \; \ell +m = n $ or the sphere $ S^{n} $. This classification is achieved by applying constraints to the tangent and normal components of the immersion.
Citation: Ibrahim Al-dayel. Investigating the characteristics of Clifford hypersurfaces and the unit sphere via a minimal immersion in $ S^{n+1} $[J]. AIMS Mathematics, 2024, 9(10): 26951-26960. doi: 10.3934/math.20241311
In this article, we find the different sufficient conditions for a compact minimal hypersurface $ M $ of the unit sphere $ S^{n+1}, n\in \mathbb{Z}^{+} $ to be the Clifford hypersurface $ S^{\ell }(\sqrt{\frac{\ell }{n}})\times S^{m}(\sqrt{\frac{m}{n}}), $ where $ \ell, m\in \mathbb{Z}^{+}, \; \ell +m = n $ or the sphere $ S^{n} $. This classification is achieved by applying constraints to the tangent and normal components of the immersion.
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Ibrahim Al-dayel. Investigating the characteristics of Clifford hypersurfaces and the unit sphere via a minimal immersion in $ S^{n+1} $[J]. AIMS Mathematics, 2024, 9(10): 26951-26960. doi: 10.3934/math.20241311
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